By applying six nuclear microsatellites [11,12] (table 1) in two wild cherry stands, we obtained different proportions of distinguishable genotypes. In the stand of Roringen, which is managed as a HFS, 48 different multilocus genotypes were found among 56 analyzed adult individuals. In Wibbecke, however, a relic stand of a former CWS, we observed only 24 multilocus genotypes among 78 P. avium trees.
For both stands we found a mean number of 5.5 alleles per locus. The stands differed for their diversity measures: In Roringen a gene pool diversity of 2.88 (ranging from 2.01 to 4.02 among the individual loci) and in Wibbecke a gene pool diversity of 3.00 (ranging from 1.51 to 4.86 among the individual loci) was found (Table 1). Combined into the hypothetical gametic diversity, this yielded values of 649.24 and 1306.24 for Roringen and Wibbecke, respectively. This suggests generally higher efficiencies for the identification of clones in Wibbecke than in Roringen. The allele frequencies that are the basis for the following statistical calculations concerning clonal vs. sexual reproduction are listed in Table 2.
In order to obtain information whether identical multilocus genotypes belong to the same clone, the testing procedure C2N was applied to the common characterization of sexual reproduction by random gene association, which is determined by a relative gene association Ar(g) = 0 (Table 3 and 4). The values for C2N ranged from 1.8033 · 10-6 to 2.4674 · 10-11 in Roringen and 7.9074 · 10-6 to 3.1075 · 10-13 in Wibbecke for all genotypes observed in at least two copies, which are consistently highly significant. Particularly low values were calculated for CnN, indicating that the probability of exclusively sexual reproduction within groups of identical genotypes tends towards zero. Hence, all copies of genotypes observed in both stands are suggested to be due to clonal propagation.
Based on the absence of gene associations, the degree of clonal propagation measured as the average number of individuals (ramets) per clone (genet cloning success) (i.e. N/G, with N = number of individuals and G = number of clones or genets) thus yields estimates 56/48 (= 1.166) and 78/26 (= 3.00) in Roringen and Wibbecke, respectively. These estimates are to be considered as minimum values, since, with low probability, the copies of a genotype may contain further clones.
The highly significant values for C2N, however, turned out to be misleading when additional markers were supplied. Such „Type one errors“ were detected for the multilocus genotypes Ror1, Wib1, Wib3, Wib4 and Wib6 (Table 3) after the analysis of two additional microsatellites in Roringen and six polymorphic isozymes in Wibbecke. By the above explanations this is highly likely to be due to the inappropriateness of the assumption Ar(g) = 0. As shown above, removal of the error requires an increase of Ar to at least guarantee that C2N(H) ≥ ε. This threshold value of Ar was computed for each of the multilocus genotypes that occurred at least twice within the two wild cherry stands and that are thus candidates for clonal propagation.
Since all genotypes are heterozygous for at least one gene locus, the largest lower bound α equals 0 for all genotypes according to equation 1 in the additional file. The least upper bound ω(g) ranges from 0.054 to 0.268 in Roringen and from 0.038 to 0.282 in Wibbecke (see Table 4). The highest ω-values were obtained for multilocus genotypes for which a Type one error was detected (ω(g) ranging from 0.166 to 0.282). Among those genotypes with large ω-values no Type one error was detected for only three (with the exceptions Ror4, Wib7 and Wib10, with ω(g) ranging from 0.224 to 0.282). The majority of genotypes for which no Type one error was detected therefore showed the lowest ω-values. Since a small ω-value for a genotype indicates that its alleles are rare (and so the genotype itself), this accords with the expectation that copies of such genotypes belong to a single clone. This is also reflected by the frequencies of genotypes hypothesized to result from random gene association (see Table 4).
For the five genotypes for which a Type one error was detected, Table 4 also gives the lower bound of the relative gene association Ar(g) that would have avoided the Type one error. These lower bounds result as the smallest value of Ar for which C2N = 0.05. The bounds were in a first step obtained graphically by plotting C2N as a function of Ar (see figure 1). Subsequently this value was made more precise by computational approximation. The differences in the graphs of figure 1 are due to the differences in allele frequencies and the resulting least upper bounds (ω(g)) for the respective MLGs. Because of the very small expected frequencies of the MLGs the differences in the graphs are mainly due to the differences in the least upper bounds ω, such that in effect the graphs become steeper with increasing ω.
Assuming that the largest of these lower bounds of relative gene association (Ar = 0.0275) is not exceeded by any of the genotypes found in at least two copies, the significance probabilities C2N were re-calculated. The re-calculation is based on the genotypes determined for the initial six microsatellite loci. The result is shown in the rightmost column of Table 4, and it demonstrates that it cannot be ruled out that three of the genotypes for which a Type one error was not detected for Ar = 0 consist of more than one clone at the significance level ε = 0.05. These three genotypes are exactly those which complete the group of genotypes with the distinctly largest ω-values.
The stand with the larger degree of clonal propagation (Wibbecke) is also the one with the higher measures of genetic diversity for both the gene pool and the hypothetical gametic pool (see Table 1). Since, as was mentioned above, higher genetic diversity increases the likelihood of detecting clones, this hints at the possibility that the number of clones detected in Roringen is underestimated. The reasoning of this expectation lies in the fact that only among genetically identical individuals additional ramets belonging to different clones can be expected to exist, and that this possibility is indicated by a significance probability that exceeds the level of significance (i.e. C2N ≥ ε). Yet, nothing definite can be said about the actual number of clones present among the copies of a genotype for which C2N ≥ ε holds. Hence, in the test based on Ar = 0 this is irrelevant, since for all genotypes with at least two copies the test yields significance (i.e. C2N Ar = 0.0275 for the inital six microsatellite loci.
Calculating cloning success in the two stands with all the additional information (application of further markers and considering gene association), we revealed slightly modified results for the HFS (N/G = 56/49 = 1.143 instead of 1.166) and larger differences for the CWS (N/G = 78/34 = 2.290 instead of 3.000). The same holds for Simpson's index of concentration C. The probability to draw two individuals with the same MLG decreases for both stands, slightly for the HFS (from C = 0.008 to C = 0.007) and distinctly for the CWS (from C = 0.067 to 0.051).
Looking at the map in figure 2, the clonal groups in Roringen are found in clusters or chains, whereas the distribution of the ramets of several single clones in Wibbecke shows larger spatial spread (about 90 m for the genet Wib 1a and about 75 m for Wib 8) and intermingling (Wib 3a, Wib 3b).
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